"All men have stars, ...but they are not the same things for
different people. For some, who are travelers, the stars are guides. For others, they are
no more than little lights in the sky. For others, who are scholars, they are
problems....."

We will quote distances in parsecs, abbreviated as pc, for much of the rest
of the course; for really large distances we will use a unit of kpc (kiloparsecs - 1000pc)
or Mpc (megaparsecs - 1,000,000pc).

The only direct way to measure stellar distances is through
parallaxes - the change in direction toward a nearby star due to our change in position as
the earth goes around its orbit. See how the parallax is reduced when the distance of the
star increases in this animation.

After Kepler and Newton, it was obvious
that parallax should be observable, but it was still nearly two
centuries before a stellar parallax was first measured -- by Bessel in 1838.
The problem was that the stars are so distant that parallax is very small and difficult to
measure.

Bessel selected a star with a large proper motion because
he reasoned that it would be likely to be near the solar system.

The stars are all moving
rapidly through space. Why is this motion only apparent for nearby ones? Although these
two stars are moving at the same speed, notice how the nearer one appears to the
astronomer to have gone much further in the same time.(animation by G.
Rieke)

This gave him two images of the field. He could offset these images to
superimpose the images of two different stars and then measure their separation by the
amount of lens offset required to bring the images together. In this way, and with great
care and perseverance he was able to make accurate measurements.

Distances can be deduced indirectly in many other ways. For example, if many stars are together in a cluster, they will all
be at the same distance and if we can figure out the distance for one, we know
it for all of them.

The luminosity of a star is one of its fundamental parameters -- the
luminosity is a direct measure of the rate at which nuclear fusion is proceeding in the
star's core.

Astronomers tend to use
a logarithmic scale for brightness called magnitudes. We will not
use them in this course, but if you are taking another astronomy course and using our
notes for review, for example, you can learn how they work here

Luminosity, apparent brightness, and distance are linked through the radiation
laws, so if we know any two we can compute the third - for example, if we can estimate the
luminosity without knowing the distance and can measure the apparent brightness, we can
calculate the distance.

Annie Jump Cannon developed the system of stellar
classification used today and published the 9 volumes of the "Henry Draper
Catalog" classifying 225,000 stars. She managed to maintain uniform criteria for this
whole work!

Cannon's system ranked the stars alphabetically in
order of the strength of their hydrogen absorption lines, with the strongest
A0...A9, B0...B9, C.., etc.

It became obvious near the end of this work that the
differences in the low resolution spectra used for classification were dominated by
temperature differences.
The hydrogen lines are strongest for intermediate temperatures, near 10,000K. At higher
temperatures, the electrons are stripped from the nuclei and there are no lines, while at
lower temperatures the atoms are in their "ground" state and cannot absorb
efficiently in the optical lines. In order of temperature, high to low, Cannon's system
comes out:

O, B, A,
F, G, K, M.

30,000oK ------------------------->3,000oK

Sometimes recited as:

Oh, be a fine girl, kiss me.

Cecilia Payne-Gaposhkin worked out the physics that
proved that the stars are all mostly made of hydrogen and that the sequence of stellar
spectral types is a temperature sequence.

Why didn't "Miss Cannon" use
the colors and Wien's Law to get temperatures?

There is dust between the stars that makes them look more red than
they really are, and by amounts that vary in unpredictable ways.

From the Stefann-Boltzmann
Law, E=AT4, (energy from a blackbody is equal to a
constant times the area of the blackbody times the temperature to the fourth power),
we could estimate a star's luminosity IF we also knew its surface area (which we rarely
do!):

By plotting the orbit and measuring the period,
Kepler's Law can be used to determine the masses of the stars:

-- here P is the period of the orbits of the stars around each other, a
is their separation, G is the gravitational constant, and their masses are M1
and M2 (technically this gives only the sum of the masses of the two stars but
by making a few other measurements such as radial velocities the actual values can be
determined).

Spectroscopic
binaries are pairs too close together to be seen as separate stars, but whose spectral
lines can be seen separately (and which move relative to each other as the stars move
around their orbits):

Here the horizontal axis is labeled with temperature in place of
color. According to the radiation laws, a very luminous cool star must be very large,
while a very hot but low luminosity star must be very small. From Gene Smith,
http://casswww.ucsd.edu/public/tutorial/

Perhaps in the discussion above you noticed a change in
the type of astronomer involved